Factual error: "Ice Station Zebra" is one of dozens of films which make the mistake of showing people carrying rifles such as M-16s with the magazines inserted. In the scene where Marine Captain Jim Brown arrives at the submarine via helicopter, he comes aboard passing his M-16 through a hatch with the magazine inserted, barrel first - a double safety violation. I first saw the movie in a Marine Corps base theater, and all of us yelled at the screen when we saw that.
Plot hole: Patrick McGoohan shoots the marine captain thinking him to be the traitor, thus, McGoohan believes, stopping the marine killing Ernest Borgnine. But shortly afterwards McGoohan comes out of the hut and addresses Borgnine sarcastically as 'Comrade'. How did he know he was the real traitor? Nothing has yet happened that should cause him to see this truth.
Revealing mistake: As Patrick McGoohan walks up the steps with a homing device, a crowbar swings out and strikes him in the head. Ernest Borgnine stops the swing just before striking McGoohan's head and McGoohan's acting takes over with him jerking his head back as seen in slow motion while falling down the stairs.
Factual error: Mr Jones explains that the Russian spy satellite malfunctioned; that instead of the rocket motor pointing forward to de-orbit the camera, it pointed quit a bit to the side and effected a plane-change, i.e., it steepened the orbit's angle of inclination to Earth's equator, moving the satellite to a polar orbit, an unplanned event which made it possible for the film to come down north of the Arctic Circle. Unfortunately, orbital plane-changes are extremely costly in terms of rocket propellant (it's the reason space shuttle Columbia, on its last flight, was unable to rendezvous with the space station). There's absolutely no way that the satellite had enough propellant aboard to make more than a trivially small change in inclination, and even then it would have had nothing left to de-orbit and come back down.
Continuity mistake: When the sub surfaces at Zebra it is shown running up a tower. When we next switch to a close-up there is no tower and it is running up an antenna.
Continuity mistake: Their first attempt to punch through the ice occurs in an area where the water depth is stated as 140 feet. After bouncing off the ice the sub submerges down below 200 feet and is still descending as it moves away.
Continuity mistake: When the nuclear sub Tigerfish submerges for the first time it is at dusk in rough seas. When they cut to an underwater shot looking up at the sub the water is very calm and light. Cut back to a surface shot of the tower submerging and it's once again dusk and rough seas.
Other mistake: 3/4 day mission to the North Pole, no-one grows a millimetre of stubble or has anything to eat.